In this paper, an algorithm is presented for identification of real eigenvalues on right half of the s-plane, for linear systems, hence determining instability of the system. The proposed approach is based on Gerschgorin theorem and a new approach of Bisection method. The method is efficient since there is no need to determine all real eigenvalues and also characteristic polynomial of the system matrix. It has been found that in some class of control system problems, the method needs minor... Topics: Instability, System matrix, Gerschgorin theorem, Bisection method, Power system problem.